Generally 9 speed rings have been compatible with running 10 speed chains for a couple of years, especially since the granny ring has no shift ramps on it, but what you could run into is issues with the front derailleur cage rubbing in some gears with the 22T granny, and a slightly slower upshift since the 10 speed FD cage will be pushing on the chain in a different place on upshifts.

What you could do is buy the 10 speed set of chainrings and a 22T 9 speed granny to try it out and see if you have issues in the gear combo you ride.